Twisted phases, external fields

Both cholesteric and smectic mesophases are layered. In the former case, the periodicity arises from a natural twist to the director field, and in the latter, from a center-of-mass correlation in one dimension. There are many types of smectic phases distinguished by their symmetry and order. The set of field-induced phenomena is quite different for these two materials, owing primarily to the very different layer compressibility. That is, the cholesteric pitch can be unwound by an external field, whereas the smectic layering is typically too strong to be altered significantly. However, because of the common layered structure, there are also strong similarities. 

The analog of the magnetic intensity H (produced by external currents) would be an external field coupled to the two components of curl n. A local microscopic source of bend [23] is not easy to imagine. On the other hand, chirality is naturally coupled to twist chiral mesogens develop a spontaneous twist in the nematic phase. The cholesteric is thus analogous to a normal metal in a magnetic field. 

The spatial and temporal response of a nematic phase to a distorting force, such as an electric (or magnetic) field is determined in part by three elastic constants, kii, k22 and associated with splay, twist and bend deformations, respectively, see Figure 2.9. The elastic constants describe the restoring forces on a molecule within the nematic phase on removal of some external force which had distorted the nematic medium from its equilibrium, i.e. lowest energy conformation. The configuration of the nematic director within an LCD in the absence of an applied field is determined by the interaction of very thin layers of molecules with an orientation layer coating the surface of the substrates above the electrodes. The direction imposed on the director at the surface is then... 

The molecular orientation (i.e., the director) in liquid crystal materials can be deformed under the influence of mechanical shear or the action of an external electric or magnetic field. Deformations to the director can be classified in three different ways as there are only three ways in which the nematic ordering can be deformed. These are known as splay, twist, and bend. (Note that in this section, we consider only the nematic phase for simplicity.)... 

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